'Public interest irrelevant'

The athlete's father Henke Pistorius said it "should not have gone this far", AFP news agency reports.

"Oscar is strong, he has to be strong, he grew up like that. There's lots of things in life, especially for a man like him that is... not fair," he is quoted as saying.

Prosecutors argued that Judge Masipa misinterpreted the law when she cleared Pistorius of murder on the basis that he did not intentionally shoot Ms Steenkamp. Judge Masipa granted the appeal in the ruling in a Pretoria court on Wednesday.

"I cannot say... that the prospect of success at the Supreme Court of Appeal is remote," she said.

However, Judge Masipa dismissed the prosecution's argument that the sentence should be reviewed because Ms Steenkamp's parents had been extremely dissatisfied with it.

She also said the public interest in the case was "irrelevant" and she had ruled only on the basis of the prosecutors' case.

In court - By Pumza Fihlani, BBC News, Pretoria

Today was a big win for the state prosecutors. Although they lost their bid on the sentence, Judge Thokozile Masipa gave the go-ahead for them to appeal the conviction. This was always Gerrie Nel's main intention.

The Supreme Court of Appeal (SCA) will now decide if the principles of law were applied correctly.

A panel of up to five judges has the power to not only overturn Judge Masipa's conviction but can also rule on a minimum sentence - which in the case of murder would be 15 years in prison.

Although the sentence appeal was denied, veteran advocate Mannie Witz told me that before the SCA this would make little difference. The appeal judges' power is such that they can also consider the sentence and find that the appeal should have been granted.

For Pistorius, this means the case is far from over and if the state has its way, the worst is yet to come.

Outlining his case on Tuesday, prosecutor Gerrie Nel said the sentence was "shockingly inappropriate and does not fit the crime and the accused".

Pistorius could be eligible for parole and house arrest after serving 10 months of his five-year sentence.

He will remain in prison while the appeal process takes place.

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His father said the athlete was "strong" in prison

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Reeva Steenkamp had been going out with Pistorius for three months before the fatal shooting

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Prosecutor Gerrie Nel said in his application to appeal that the judgement was "shockingly inappropriate"

Prosecution spokesman Nathi Mncube welcome the judge's ruling on Wednesday but said prosecutors would still attempt to challenge the sentence.

The prosecution had called for the maximum 15-year sentence for culpable homicide, or manslaughter.

Ms Steenkamp, a model and law graduate, was shot dead at Pistorius' home in Pretoria in the early hours of Valentine's Day last year. He said he feared there was an intruder.

Pistorius was acquitted by Judge Masipa of both premeditated murder and the lesser murder charge of dolus eventualis, also known as common-law murder.

In South African law, this charge applies if the accused knew they might kill someone but still went ahead with their course of action.

Pistorius is serving the sentence in the hospital wing of Pretoria's Kgosi Mampuru II prison.